Question 709195
We can represent the 4 digit number as aabb.
The number can be written as 1000a + 100a + 10b + b, and this number is a perfect square:
N = 1100a + 11b = 11(100a + b)
So the number must be a multiple of 11
The multiples of 11 which result in 4 digit numbers are 33, 44, 55, 66, 77, 88 and 99
Of these, only one fills the requirement: 88^2 = 7744